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We propose a model where Dirac neutrino mass is obtained from small vacuum expectation value (VEV) of neutrino-specific Higgs doublet without fine-tuning problem. The small VEV results from a seesaw-like formula with the high energy scale identified as the Peccei-Quinn (PQ) symmetry breaking scale. Axion can be introduced à la KSVZ or DFSZ. The model suggests neutrino mass, solution to the strong CP problem, and dark matter may be mutually interconnected.